Method for producing a second harmonic wave generating device

ABSTRACT

A second harmonic wave generating device of a thin film waveguide structure having a high conversion efficiency, which satisfies the following equation: ##EQU1## wherein λμm: fundamental wavelength 
     T μm: thickness of the thin film waveguide layer 
     n OS1  : ordinary refractive index of the substrate at the fundamental wavelength 
     n OF1  : ordinary refractive index of the thin film waveguide layer at the fundamental wavelength 
     n eS2  : extraordinary refractive index of the substrate at the second harmonic wavelength 
     n eF2  : extraordinary refractive index of the thin film waveguide layer at the second harmonic wavelength ##EQU2##

This is a division of application Ser. No. 07/452,410, filed Dec. 19,1989, U.S. Pat. No. 4,973,118.

BACKGROUND OF THE INVENTION

This invention relates to a second harmonic wave generating device(hereinafter referred to as "SHG device") of a thin film waveguidestructure with a high conversion efficiency.

A SHG device utilizes nonlinear optical effects of a nonlinear opticalmaterial to convert wavelength λ of incident laser light to wavelength1/2λ, which is outputted. Since the output light has a half wavelengthof incident light, the device can be used in an optical disc memory andCD player to achieve a 4-times increase in recording density, and can beused in a laser printer and photolithography with enhanced resolution.

Heretofore, a bulk single crystal of a nonlinear optical material usinga high-output-power gas laser as a light source has been used as a SHGdevice. However, with recent increases in demand for compact opticaldisc systems and laser printers and since gas laser requires an externalmodulator for optical modulation and is not suited for compact design, aSHG device that enables use of a semiconductor laser, which can bedirectly modulated and is lower in cost and easier to handle than gaslaser, has been in demand.

When a semiconductor laser is used as a light source, since thesemiconductor laser has a low output power of several mW to several tenmW, a SHG device of a thin film waveguide structure which has aparticularly high conversion efficiency has been required.

Generation of second harmonic optical wave using a thin film waveguidehas advantages that: (1) energy of light concentrated on the thin filmcan be utilized, (2) since optical wave is confined within the thin filmand does not diffuse, interaction is possible over a long distance, and(3) a substance, which cannot make phase matching in the bulk state,becomes able to make phase matching by utilizing mode dispersion of thinfilm (Miyama and Miyazaki; IEICE Technical Report, OQE75-6 (1975),Miyazaki, Hoshino, and Akao; Proceedings of Electromagnetic Field TheoryResearch Conference, EMT-78-5 (1978)).

However, in order to obtain a SHG device of a thin film waveguidestructure, it has heretofore been necessary to conduct experiments withsubstrates of different materials and thin film waveguide layers ofdifferent materials and thicknesses at an objective fundamentalwavelength to find conditions for generation of a second harmonic waveand to determine the structure, thus requiring very inefficient work.

The inventors have conducted intensive studies and have found that asecond harmonic wave can be generated very efficiently by satisfying aspecific relation of a fundamental wavelength (λ μm), a thickness (T μm)of the thin film waveguide layer, an ordinary refractive index (n_(oS1))of the substrate at the fundamental wavelength (λ μm), an ordinaryrefractive index (n_(oF1)) of the thin film waveguide layer at thefundamental wavelength (λ μm), an extraordinary refractive index(n_(eS2)) of the substrate at a second harmonic wavelength (λ μm/2), andan extraordinary refractive index (n_(eF2)) of the thin film waveguidelayer at the second harmonic wavelength (λ μm/2), thus accomplishing thepresent invention.

SUMMARY OF THE INVENTION

In accordance with the present invention, there is provided a SHG devicecharacterized in that a fundamental wavelength (λ μm), a thickness (Tμm) of a thin film waveguide layer, an ordinary refractive index(n_(oS1)) of the substrate at the fundamental wavelength (λ μm), anordinary refractive index (n_(oF1)) of the thin film waveguide layer atthe fundamental wavelength (λ μm), an extraordinary refractive index(n_(eS2)) of the substrate at a second harmonic wavelength (λ μm/2), andan extraordinary refractive index (n_(eF2)) of the thin film waveguidelayer at the second harmonic wavelength (λ μm/2) are represented by anequation ##EQU3## wherein, N₁ in Equation (A) above is ##EQU4## and N₂in Equation (B) above is ##EQU5##

The inventive SHG device comprising a substrate and a thin filmwaveguide layer formed on the substrate, which has a structure thatsatisfies the above Equation (A) or (B) of the ordinary refractiveindices to a fundamental wave and the extraordinary refractive indicesto a second harmonic wave of the substrate and the thin film waveguidelayer, and of the thickness of the thin film waveguide layer, cangenerate the second harmonic wave of a specific fundamental wavelength.

The inventive SHG device must have a thin film waveguide layer formed ona substrate.

This is not only because generation of the second harmonic wave in theSHG device which has the thin film waveguide layer formed on thesubstrate has the advantages that the energy of light concentrated onthe thin film can be utilized and, since the optical wave is confinedwithin the thin film and does not diffuse, interaction can be made overa long distance, but also because phase matching is possible by modedispersion of the thin film, even using a substance which cannot makephase matching when used in a bulk single crystal in a prior art SHGdevice.

In the inventive SHG device, the fundamental wavelength (λ μm), thethickness (T μm) of the thin film waveguide layer, the ordinaryrefractive index (n_(oS1)) of the substrate at the fundamentalwavelength (λ μm), the ordinary refractive index (n_(oF1)) of the thinfilm waveguide layer at the fundamental wavelength (λ μm), theextraordinary refractive index (n_(eS2)) of the substrate at the secondharmonic wavelength (λ μm/2), and the extraordinary refractive index(n_(eF2)) of the thin film waveguide layer at the second harmonicwavelength (λ μm/2) are required to satisfy the equation ##EQU6##wherein, N₁ in Equation (A) above is ##EQU7## and N₂ in Equation (B)above is ##EQU8##

This is because, in the SHG device comprising the thin film waveguidelayer formed on the substrate, the conversion efficiency to the secondharmonic wavelength is so low that cannot be used in practical use,unless the structure of the device satisfies either Equation (A) orEquation (B).

In particular, in order to obtain a high conversion efficiency to thesecond harmonic wavelength, it is preferable that the fundamentalwavelength (λ μm), the thickness (T μm) of the thin film waveguidelayer, the ordinary refractive index (n_(oS1)) of the substrate at thefundamental wavelength (λ μm), the ordinary refractive index (n_(oF1))of the thin film waveguide layer at the fundamental wavelength (λ μm),the extraordinary refractive index (n_(eS2)) of the substrate at thesecond harmonic wavelength (λ μm/2), and the extraordinary refractiveindex (n_(eF2)) of the thin film waveguide layer at the second harmonicwavelength (λ μm/2), ##EQU9## satisfy Equation (A') below, and it isparticularly advantageous to satisfy Equation (A") below. ##EQU10##wherein, N₁ in Equation (A') and Equation (A") above is ##EQU11##

On the other hand, when ##EQU12## it is preferable to satisfy Equation(B') below, and it is particularly advantageous to satisfy Equation (B")below. ##EQU13## wherein, N₂ in Equation (B') and Equation (B") above is##EQU14##

In the inventive SHG device, it is preferable that incident angle (θ) ofthe fundamental wave to the optical axis (Z-axis) of the thin filmwaveguide layer is within the range 0°±15° or 90°±15°.

This is because, when the incident angle (θ) of the fundamental wave iswithin the above range, the conversion efficiency to the second harmonicis extremely high. It is particularly advantageous that the incidentangle of the fundamental wave is within the range 0°±5° or 90°±5°.

Wavelength (λ) of the fundamental wave incident to the inventive SHGdevice is preferably 0.4 to 1.6 μm.

This is because, although a shorter wavelength is more advantageous asthe fundamental wavelength (λ), generation by a semiconductor laser oflaser wave shorter in wavelength than 0.4 μm is substantially difficultand, when a fundamental wave longer in wavelength than 1.6 μm is used,since the obtained second harmonic wavelength is 1/2 the fundamentalwavelength, it is within a wavelength range that can be easily generateddirectly by a semiconductor laser, which has no advantages of use of theSHG device. It is advantageous that the wavelenth (λ) of the fundamentalwave is 0.6 to 1.3 μm which is relatively easy to obtain a semiconductorlaser light source and, in particular, 0.68 to 0.94 μm is practicallypreferable.

The inventive SHG device preferably has a thickness (T) of the thin filmwaveguide layer of 0.1 to 20 μm.

This is because, when the thickness (T) of the thin film waveguide layeris smaller than 0.1 μm, it is difficult to apply the fundamental waveand, due to a low incident efficiency, it is difficult to obtain asubstantially high SHG conversion efficiency. On the other hand, whenthe thickness (T) is greater than 20 μm, it has a low optical powerdensity and hence a low SHG conversion efficiency. Either case isundesirable for a SHG device. It is particularly advantageous that thethin film waveguide layer has a thickness of 0.5 to 10 μm, and athickness of 1 to 8 μm is practically preferable.

A variety of optical materials can be used in the substrate and thinfilm waveguide layer used in the present invention; the thin filmwaveguide layer can be made of, for example, LiNbO₃, Ba₂ NaNb₅ O₁₅, K₂LiNb₅ O₁₅, Ba₂ LiNb₅ O₁₅, Sr_(1-x) Ba_(x) Nb₂ O₆ (SBN), α-quartz,kTiOPO₄ (KTP), βBaB₂ O₄ (BBO), KB₅ O₈.4H₂ O (KB₅), KH₂ PO₄ (KDP), KD₂PO₄ (KD*), NH₄ H₂ PO₄ (ADP), C₅ H₂ AsO₄ (CDA), C₅ D₂ AsO₄ (CD*A), RbH₂PO₄ (RDP), RbH₂ AsO₄ (RDA), BeSO₄.4H₂ O, LiClO₄.3H₂ O, LiIO₃, α-LiCdBO₃,LiB₃ O₅ (LBO), urea, poly-p-nitroaniline (p-PNA), poly-diacetylene(DCH), 4-(N,N-dimethylamino)-3-acetamidonitrobenzene (DAN),4-nitrobenzaldehyde-hydrazine (NBAH),3-methoxy-4-nitrobenzaldehyde-hydrazine, 2-methyl-4-nitroaniline (MNA),or the like; and the substrate can be made of, for example, LiTaO₃,MgO,Gd₃ Ga₅ O₁₂ (GGG), Nd₃ Ga₅ O₁₂ (NdGG), Sm₃ Ga₅ O₁₂ (SmGG), SiO₂,alumina, KTP, BBO, LBO, DKP, or the like, sode glass, borosilicateglass, polymethylmethacrylate (PMMA), or the like.

These materials for the substrate and the thin film waveguide layer canbe combined with a different element such as Na, Cr, Mg, Nd, Ti or thelike to adjust their refractive indices.

Such a different element as Na, Cr, Mg, Nd, Ti or the like is addedpreferably using the procedure, in which the raw material and theimpurity are previously mixed, and the thin film waveguide layer isformed on the substrate by such as a LPE (liquid phase epitaxial)technique, or, a diffusion technique is used to diffuse an impurity suchas Na, Mg, Nd, Ti or the like into the the substrate or the thin filmwaveguide layer.

Material combinations of thin film waveguide layer/substrate suitablefor use in the inventive SHG device include LiNbO₃ /LiTaO₃,2-methyl-4-nitroaniline (MNA)/alumina; KTiOPO₄ (KTP)/alumina, β-BaB₂ O₄(BBO)/alumina; 4-(N,N-dimethylamino)-3-acetamidonitrobenzene (DAN)/SiO₂; 4-(N,N-methylamino)-3-acetamidonitrobenzene(DAN)/polymethylmethacrylate (PMMA); LiB₃ O₅ (LBO)/BBO; LBO/alumina;RbH₂ PO₄ (RDP)/KH₂ PO₄ (KDP); and poly-p-nitroaniline (p-PNA)/PMMA.

Above all, a combination of LiTaO₃ for the substrate with LiNbO₃ for thethin film waveguide layer is particularly preferable for use in the SHGdevice.

This is because the LiNbO₃ is large in nonlinear optical constant andsmall in optical loss, and can be formed into a uniform thin film, andLiTaO₃ is similar in crystal structure to the LiNbO₃, easy to form athin film of LiNbO₃ on it, and easy to obtain a high-quality,inexpensive crystal.

The inventive SHG device is preferably of a channel type waveguide witha width of 1 to 10 μm. The reason why a SHG device using a channel-typewaveguide is advantageous is that this type of device can have a highoptical power density over a slab type. The reason why a width of 1 to10 μm is advantageous is that a width smaller than 1 μm is difficult tointroduce incident light into the waveguide and low in incidentefficiency, resulting in a low SHG conversion efficiency, and, althougha larger width has a higher incident efficiency, a width greater than 10μm is low in optical power density, resulting in a low SHG conversionefficiency.

The inventive SHG device can be produced by forming the thin filmwaveguide layer on the substrate by sputtering or a liquid phaseepitaxial method. Furthermore, on top of the thin film waveguide layer,a Ti waveguide pattern can be formed by photolithography and RFsputtering, which can be used as an etching mask in ion beam etching toform a channel-type SHG device.

DESCRIPTION OF PREFERRED EMBODIMENTS

Examples of the present invention will now be described in detail.

EXAMPLE 1-1

For a fundamental wavelength (λ) of 0.83 μm, a LiNbO₃ single crystalthin film comprising a solid solution with 1 mole % each of Nd and Nahaving an ordinary refractive index (n_(oF1)) of 2.270 at thefundamental wavelength and an extraordinarly refractive index (n_(eF2))of 2.263 at the second harmonic wavelength was grown by a liquid phaseepitaxial method to a thickness of 1.80 μm on a 0.5 mm thick X-cutLiTaO₃ single crystal substrate having an ordinary refractive index(n_(oS1)) of 2.151 at the fundamental wavelength and an extraordinaryrefractive index (n_(eS2)) of 2.261 at the second harmonic wavelength,and an optical device was fabricated using the thin film as a slab-typewaveguide. Both end faces of the device were mirror-finished to allowtransmission of light through the end faces, thus forming a SHG device.This SHG device corresponds to the case of {(λ+0.1)N₁ /(λ³ T)}=0.2.

To the SHG device, a 50 mW semiconductor laser of 0.83 μm in wavelengthwas applied with an incident angle of 90° with respect to the opticalaxis (Z-axis) of the Nd/Na-containing LiNbO₃ single crystal thin film.As a result, the SHG device exhibited a SHG conversion efficiency of18.8%, showing that it is a SHG device with an extremely high SHGconversion efficiency.

EXAMPLE 1-2

Using the same procedure as in above Example 1-1, a SHG device wasfabricated using a LiNbO₃ single crystal thin film having a thickness of7.23 μm. This SHG device corresponds to the case of {(λ+0.1)N₁ /(λ³T)}=0.05.

This SHG device was measured for the SHG conversion efficiency as inExample 1-1 and found to have a SHG conversion efficiency of 1.4%,showing that it is a SHG device with a sufficiently high SHG conversionefficiency.

EXAMPLE 1-3

Using the same procedure as in above Example 1-1, a SHG device wasfabricated using a LiNbO₃ single crystal thin film having a thickness of0.24 μm. This SHG device corresponds to the case of {(λ+0.1)N₁ /(λ³T)}=1.5.

This SHG device was measured for the SHG conversion efficiency as inExample 1-1 and found to have a SHG conversion efficiency of 2.5%,showing that it is a SHG device with a sufficiently high SHG conversionefficiency.

EXAMPLE 1-4

An etching mask of 5.0 μm in width was formed using a photoresist filmon the single crystal thin film of the SHG device obtained in Example1-1, which was then ion beam-etched to fabricate a channel-type SHGdevice.

This SHG device was measured for the SHG conversion efficiency as inExample 1-1 and found to have a SHG conversion efficiency of 33.0%,showing that it is a SHG device with an extremely high SHG conversionefficiency.

EXAMPLE 2-1

For a fundamental wavelength (λ) of 0.83 μm, a LiNbO₃ single crystalthin film having an ordinary refractive index (n_(oF1)) of 2.253 at thefundamental wavelength and an extraordinary refractive index (n_(eF2))of 2.249 at the second harmonic wavelength was grown by a RF sputteringmethod to a thickness of 3.15 μm on an Al₂ O₃ single crystal substratehaving an ordinary refractive index (n_(oS1)) of 1.759 at thefundamental wavelength and an extraordinary refractive index (n_(eS2))of 1.779 at the second harmonic wavelength, and an optical device wasfabricated using the thin film as a slab-type waveguide. Both end facesof the device were mirror-finished to allow transmission of lightthrough the end faces, thus forming a SHG device. This SHG devicecorresponds to the case of {(λ+0.1)N₂ /(λ³ T)}=0.5.

To the SHG device, a 40 mW semiconductor laser of 0.83 μm in wavelengthwas applied with an incident angle of 90° with respect to the opticalaxis (Z-axis) of the LiNbO₃ single crystal thin film. As a result, theSHG device exhibited a SHG conversion efficiency of 12.2%, showing thatit is a SHG device with an extremely high SHG conversion efficiency.

EXAMPLE 2-2

Using the same procedure as in above Example 2-1, a SHG device wasfabricated using a LiNbO₃ single crystal thin film having a thickness of0.45 μm. This SHG device corresponds to the case of {(λ+0.1)N₂ /(λ³T)}=3.5.

This SHG device was measured for the SHG conversion efficiency as inExample 2-1 and found to have a SHG conversion efficiency of 1.7%,showing that it is a SHG device with a sufficiently high SHG conversionefficiency.

EXAMPLE 2-3

Using the same procedure as in above Example 2-1, a SHG device wasfabricated using a LiNbO₃ single crystal thin film having a thickness of8.74 μm. This SHG device corresponds to the case of {(λ+0.1)N₂ /(λ³T)}=0.18.

This SHG device was measured for the SHG conversion efficiency as inExample 2-1 and found to have a SHG conversion efficiency of 1.2%,showing that it is a SHG device with a sufficiently high SHG conversionefficiency.

EXAMPLE 3-1

For a fundamental wavelength (λ) of 0.90 μm, a SBN25 (Sr₀.25 Ba₀.75 Nb₂O₆) thin film having an ordinary refractive index (n_(oF1)) of 2.250 atthe fundamental wavelength and an extraordinary refractive index(n_(eF2)) of 2.225 at the second harmonic wavelength was grown by a RFsputtering method to a thickness of 2.29 μm on a NdGG (Nd₃ Ga₅ O₁₂)single crystal substrate having an ordinary refractive index (n_(oS1))of 1.965 at the fundamental wavelength and an extraordinary refractiveindex (n_(eS2)) of 1.979 at the second harmonic wavelength, and anoptical device was fabricated using the thin film as a slab-typewaveguide. Both end faces of the device were mirror-finished to allowtransmission of light through the end faces, thus forming a SHG device.This SHG device corresponds to the case of {(λ+0.1)N₂ /(λ³ T)}=0.52.

To the SHG device, a 50 mW semiconductor laser of 0.90 μm in wavelengthwas applied with an incident angle of 0° with respect to the opticalaxis (Z-axis) of the SBN thin film. As a result, the SHG deviceexhibited a SHG conversion efficiency of 17.8%, showing that it is a SHGdevice with an extremely high SHG conversion efficiency.

EXAMPLE 3-2

Using the same procedure as in above Example 3-1, a SHG device wasfabricated using a SBN25 thin film having a thickness of 0.30 μm. ThisSHG device corresponds to the case of {(λ+0.1)N₂ /(λ³ T)}=4.0.

This SHG device was measured for the SHG conversion efficiency as inExample 3-1 and found to have a SHG conversion efficiency of 1.1%,showing that it is a SHG device with a sufficiently high SHG conversionefficiency.

EXAMPLE 3-3

Using the same procedure as in above Example 3-1, a SHG device wasfabricated using a SBN25 thin film having a thickness of 3.95 μm. ThisSHG device corresponds to the case of {(λ+0.1)N₂ /(λ³ T)}=0.3.

This SHG device was measured for the SHG conversion efficiency as inExample 3-1 and found to have a SHG conversion efficiency of 4.5%,showing that it is a SHG device with a sufficiently high SHG conversionefficiency.

EXAMPLE 4-1

For a fundamental wavelength (λ) of 0.67 μm, a KNbO₃ single crystal thinfilm having an ordinary refractive index (n_(oF1)) of 2.320 at thefundamental wavelength and an extraordinary refractive index (n_(eF2))of 2.319 at the second harmonic wavelength was grown by a liquid phaseepitaxial method to a thickness of 4.10 μm on a KTP (KTiOPO₄) singlecrystal substrate having an ordinary refractive index (n_(oS1)) of 1.860at the fundamental wavelength and an extraordinary refractive index(n_(eS2)) of 1.822 at the second harmonic wavelength, and an opticaldevice was fabricated using the thin film as a slab-type waveguide. Bothend faces of the device were mirror-finished to allow transmission oflight through the end faces, thus forming a SHG device. This SHG devicecorresponds to the case of {(λ+0.1)N₂ /(λ³ T)}=0.67.

To the SHG device, a 5 mW semiconductor laser of 0.67 μm in wavelengthwas applied with an incident angle of 90°. As a result, the SHG deviceexhibited a SHG conversion efficiency of 13.8%, showing that it is a SHGdevice with an extremely high SHG conversion efficiency.

EXAMPLE 4-2

Using the same procedure as in above Example 4-1, a SHG device wasfabricated using a KTP thin film having a thickness of 0.69 μm. This SHGdevice corresponds to the case of {(λ+0.1)N₂ /(λ³ T)}=4.0.

This SHG device was measured for the SHG conversion efficiency as inExample 3-1 and found to have a SHG conversion efficiency of 1.1%,showing that it is a SHG device with a sufficiently high SHG conversionefficiency.

EXAMPLE 4-3

Using the same procedure as in above Example 4-1, a SHG device wasfabricated using a KTP thin film having a thickness of 9.18 μm. This SHGdevice corresponds to the case of {(λ+0.1)N₂ /(λ³ T)}=0.3.

This SHG device was measured for the SHG conversion efficiency as inExample 3-1 and found to have a SHG conversion efficiency of 1.2%,showing that it is a SHG device with a sufficiently high SHG conversionefficiency.

EXAMPLE 5-1

For a fundamental wavelength (λ) of 0.488 μm, a BBO (β-BaBO₄) thin filmhaving an ordinary refractive index (n_(oF1)) of 2.262 at thefundamental wavelength and an extraordinary refractive index (n_(eF2))of 2.256 at the second harmonic wavelength was grown by a RF sputteringmethod to a thickness of 5.24 μm on a LBO (LiB₃ O₅) substrate having anordinary refractive index (n_(oS1)) of 1.965 at the fundamentalwavelength and an extraordinary refractive index (n_(eS2)) of 1.979 atthe second harmonic wavelength, and an optical device was fabricatedusing the thin film as a slab-type waveguide. Both end faces of thedevice were mirror-finished to allow transmission of light through theend faces, thus forming a SHG device. This SHG device corresponds to thecase of {(λ+0.1)N₂ /(λ³ T)}=0.90.

To the SHG device, a 100 mW Ar laser of 0.488 μm in wavelength wasapplied with an incident angle of 0° with respect to the optical axis(Z-axis) of the BBO thin film. As a result, the SHG device exhibited aSHG conversion efficiency of 33.4%, showing that it is a SHG device withan extremely high SHG conversion efficiency.

EXAMPLE 5-2

Using the same procedure as in above Example 5-1, a SHG device wasfabricated using a BBO thin film having a thickness of 1.18 μm. This SHGdevice corresponds to the case of {(λ+0.1)N₂ /(λ³ T)}=4.0.

This SHG device was measured for the SHG conversion efficiency as inExample 5-1 and found to have a SHG conversion efficiency of 2.8%,showing that it is a SHG device with a sufficiently high SHG conversionefficiency.

EXAMPLE 5-3

Using the same procedure as in above Example 5-1, a SHG device wasfabricated using a BBO thin film having a thickness of 15.73 μm. ThisSHG device corresponds to the case of {(λ+0.1)N₂ /(λ³ T)}=0.3.

This SHG device was measured for the SHG conversion efficiency as inExample 5-1 and found to have a SHG conversion efficiency of 2.2%,showing that it is a SHG device with a sufficiently high SHG conversionefficiency.

As described above, the present invention can provide a SHG device of athin film waveguide structure having an extremely high SHG conversionefficiency.

We claim:
 1. A method for producing a second harmonic wave generatingdevice comprising forming a thin film on a substrate and ion beametching said thin film to form a thin film waveguide layer,characterized in that a fundamental wavelength (λμm), a thickness (Tμm)of said thin film waveguide layer, an ordinary refractive index(n_(OS1)) of said substrate at said fundamental wavelength (λμm), anordinary refractive index (n_(OF1)) of said thin film waveguide layer atsaid fundamental wavelength (λμm), an extraordinary refractive index(n_(eS2)) of said substrate at a second harmonic wavelength (λμm/2), andan extraordinary refractive index (n_(eF2)) of said thin film waveguidelayer at said second harmonic wavelength (λμm/2) are represented by anequation, ##EQU15## wherein, N₁ in Equation (A) is ##EQU16## and N₂ inEquation (B) is ##EQU17##